7-7 Answer Key

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7-7 Geometric Sequences as Exponential Functions Determine whether each sequence is arithmetic, geometric, or neither. Explain. 1. 200, 40, 8, … SOLUTION: Since the ratios are constant, the sequence is geometric. The common ratio is 2. 2, 4, 16, … SOLUTION: . The ratios are not constant, so the sequence is not geometric. There is no common difference, so the sequence is not arithmetic. Thus, the sequence is neither geometric nor arithmetic. 3. −6, −3, 0, 3, … SOLUTION: The ratios are not constant, so the sequence is not geometric. Since the differences are constant, the sequence is arithmetic. The common difference is 3. 4. 1, −1, 1, −1, … SOLUTION: Since the ratios are constant, the sequence is geometric. The common ratio is –1. Find the next three terms in each geometric sequence. 5. 10, 20, 40, 80, … SOLUTION: eSolutions Manual - Powered by Cognero Page 1 7-7 Geometric Sequences as Exponential Functions Since the ratios are constant, the sequence is geometric. The common ratio is –1. Find the next three terms in each geometric sequence. 5. 10, 20, 40, 80, … SOLUTION: The common ratio is 2. Multiply each term by the common ratio to find the next three terms. 80 × 2 = 160 160 × 2 = 320 320 × 2 = 640 The next three terms of the sequence are 160, 320, and 640. 6. 100, 50, 25, … SOLUTION: Calculate common ratio. The common ratio is 0.5. Multiply each term by the common ratio to find the next three terms. 25 × 0.5 = 12.5 12.5 × 0.5 = 6.25 6.25 × 0.5 = 3.125 The next three terms of the sequence are 12.5, 6.25, and 3.125. 7. 4, −1, ,… SOLUTION: Calculate the common ratio. The common ratio is × × × = = = . Multiply each term by the common ratio to find the next three terms. The next three terms of the sequence are 8. −7, 21, −63, … , , and . eSolutions Manual - Powered by Cognero

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